The Barcelona star stole the show with three goals to help the two-time World Cup winners earn a quality victory against Ottmar Hitzfeld's men.
The Barcelona star scored two of them late on after the match looked headed for a draw after Xherdan Shaqiri canceled out Messi's first-half strike with a goal early in the second period.
Looking to build off a win against Colombia in World Cup qualifying in November, the South Americans showed pace and creativity in the early minutes, but the team did not pose much of a threat with the ball as Ottmar Hitfeld's defense was up to the task.
Fans were forced to wait for nearly 20 minutes to see the match's first real chance aside from a poor free kick from Messi, but the wait was well worth it.
The Argentine star played Sergio Aguero at the top of the box, and the Manchester City striker rolled the ball behind him without looking to return the ball to an oncoming Messi, who controlled the effort and fired a brilliant low shot from 20 yards into the right side of the goal for the early advantage.
In the following minutes, Alejandro Sabella's men controlled the majority of the possession as they looked for their second, but the crucial pass to send a player through was missing.
The first half ended with the home team infiltrating the visiting area on numerous occasions, nearly scoring the equaliser through Granit Xhaka, who found the ball after a Shaqiri cross, drilling an effort over Sergio Romero and the crossbar from 16 yards.
In the second half, the Europeans responded quickly. In the 49th minute, Shaqiri curled the ball into the upper-right corner of the goal with one touch at the right side of the box after a cross from the left from Stephan Lichtsteiner somehow found its way to the soon-to-be Bayern Munich starlet.
With things level, both nations searched for the go-ahead goal, Aguero nearly put his team ahead with a poked shot from the middle of the box, but Marco Wolfli reacted quickly to slap the ball over the crossbar.
Messi managed to leave things late in the 42nd minute with a solo effort, running into the left side of the box before lifting a ball over the charging goalkeeper before it hit the crossbar and bounced down into the goal.
Messi added another in extra time after Gonzalo Higuain was brought down in the box, with the Rosario-born striker finishing calmly into the left side of the net, sending the Swiss custodian the other way to cement the result.
The home team next returns to action at the end of May when it hosts Germany in a friendly. The South Americans will host Ecuador in early June in a World Cup qualifying match.